Simplified a little: 
my ($num) = $_num =~ /^(0*\.\d+)$/

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 but it's still a string. Let's convert to a number: 
my $num = ($_num =~ /^(0+(?:\.\d+)?|\.\d+)$/) ? 0+$1 : undef;

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In any case, it's probably better if you first check if it's a number, then check if it's in range. It makes the code easier to read, more maintainable and less error prone. 
my ($num) = $_num =~ /^(...)$/
undef $num if defined $num && ($num < 0 || $num >= 1);

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Update: oops, it didn't match just plain '0'.

In reply to Re: Match number >= 0 and <1 by ikegami
in thread Match number >= 0 and <1 by lupey

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